{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--BOOK_INFORMATION-->\n",
    "<img align=\"left\" style=\"padding-right:10px;\" src=\"figures/PHydro-cover-small.png\">\n",
    "*This is the Jupyter notebook version of the [Python in Hydrology](http://www.greenteapress.com/pythonhydro/pythonhydro.html) by Sat Kumar Tomer.*\n",
    "*Source code is available at [code.google.com](https://code.google.com/archive/p/python-in-hydrology/source).*\n",
    "\n",
    "*The book is available under the [GNU Free Documentation License](http://www.gnu.org/copyleft/fdl.html). If you have comments, corrections or suggestions, please send email to satkumartomer@gmail.com.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--NAVIGATION-->\n",
    "< [ODE](09.02-ODE.ipynb)| [Contents](Index.ipynb) | [10. Advance Statistics](10.00-Advance-Statistics.ipynb) >"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 9.3 参数估计"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2a18eed3a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy import optimize,special\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "x = np.arange(0,10,0.01)\n",
    "for k in np.arange(0.5,5.5):\n",
    "    y = special.jv(k,x)\n",
    "\n",
    "f = lambda x:-special.jv(k,x)\n",
    "x_max = optimize.fminbound(f,0,6)\n",
    "\n",
    "plt.plot(x,y,lw=3)\n",
    "plt.plot([x_max],[special.jv(k,x_max)],'rs',ms=12)\n",
    "plt.title('Different Bessel functions and their local maxima')\n",
    "plt.show()\n",
    "plt.close()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
